Question: Rewrite as a simplified fraction. ${1.4\overline{12} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1412.1212...\\ 10x &= 14.1212...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1398}$ ${x = \dfrac{1398}{990}} $ ${x = \dfrac{233}{165}} \text{or} {1 \dfrac{68}{165}}$